Once I go to Layouts, configure the modules the way I want and select 'Save as Copy' I get the dialog box. I enter a new name and save.
Everything seems to go OK, but I can't find that clone in the Layouts drop-down.
If I do this again, and use the same name as I used the first time, I get a message that the layout already exists!
I did notice that in the template files the cloned layout does exist here: [root]/templates/t3_bs3_blank/local/tpls
I am using Joomla 3.3.1 and Bootstrap 3 version of the Blank template. I have had the same problem with the Bootstrap 2 version as well.